This article gives the potential energy function of quark in the gluon field, derives the wave function of quark in stationary state and the quark confinement and asymptotic freedom, shows that a quark is composed of ...This article gives the potential energy function of quark in the gluon field, derives the wave function of quark in stationary state and the quark confinement and asymptotic freedom, shows that a quark is composed of two different color gluons, expounds the formation mechanism of the quark confinement and asymptotic freedom and the physical substance of “colors” of quark, and discusses the stability of hadrons in the end.展开更多
The stationary phase method in conventional Lighthill＇s two-stage scheme to get the expressions of the velocity field was given up in this paper. The method that Ursell had used in deducing the elevation expression o...The stationary phase method in conventional Lighthill＇s two-stage scheme to get the expressions of the velocity field was given up in this paper. The method that Ursell had used in deducing the elevation expression of ship wave was adopted, and an asymptotic solution of velocity field of ship waves on an inviscid fluid that is perfectly fit for the region inside and outside the critical lines was obtained. It is very convenient to be used in SAR technique.展开更多
This paper studies an asymptotic solvability problem for linear quadratic(LQ)mean field games with controlled diffusions and indefinite weights for the state and control in the costs.The authors employ a rescaling app...This paper studies an asymptotic solvability problem for linear quadratic(LQ)mean field games with controlled diffusions and indefinite weights for the state and control in the costs.The authors employ a rescaling approach to derive a low dimensional Riccati ordinary differential equation(ODE)system,which characterizes a necessary and sufficient condition for asymptotic solvability.The rescaling technique is further used for performance estimates,establishing an O(1/N)-Nash equilibrium for the obtained decentralized strategies.展开更多
This paper considers the local linear estimation of a multivariate regression function and its derivatives for a stationary long memory(long range dependent) nonparametric spatio-temporal regression model.Under some m...This paper considers the local linear estimation of a multivariate regression function and its derivatives for a stationary long memory(long range dependent) nonparametric spatio-temporal regression model.Under some mild regularity assumptions, the pointwise strong convergence, the uniform weak consistency with convergence rates and the joint asymptotic distribution of the estimators are established. A simulation study is carried out to illustrate the performance of the proposed estimators.展开更多
The stress and deformation fields near the tip of a mode-I dynamic crack steadily propagating in an elastic-perfectly plastic compressible material are considered under plane strain conditions. Within the framework of...The stress and deformation fields near the tip of a mode-I dynamic crack steadily propagating in an elastic-perfectly plastic compressible material are considered under plane strain conditions. Within the framework of infinitesimal displacement gradient theory, the material is characterized by the Von Mises yield criterion and the associated J(2) flow theory of plasticity. Through rigorous mathematical analysis, this paper eliminates the possibilities of elastic unloading and continuous asymptotic fields with singular deformation, and then constructs a fully continuous and bounded asymptotic stress and strain field. It is found that in this solution there exists a parameter phi(0) which cannot be determined by asymptotic analysis but may characterize the effect of the far field. Lastly the variations of continuous stresses, velocities and strains around the crack tip are given numerically for different values of phi(0).展开更多
The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is ...The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.展开更多
A generalized form of material gradation applicable to a more broad range of functionally graded materials(FGMs) was presented.With the material model,analytical expressions of crack tip higher order stress fields in ...A generalized form of material gradation applicable to a more broad range of functionally graded materials(FGMs) was presented.With the material model,analytical expressions of crack tip higher order stress fields in a series form for opening mode and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis.Then,a numerical experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite element analysis by local collocation and then comparing the estimations with the existing solution.The expressions show that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects on crack tip stress fields in the case of FGMs.The numerical experiment further confirms that the addition of the nonhomogeneity specific terms in the expressions not only improves estimates of stress intensity factor,but also gives consistent estimates as the distance away from the crack tip increases.Hence,the analytical expressions are suitable for the representation of crack tip stress fields and the analysis of full field data.展开更多
Let K be an algebraic number field of finite degree over the rational field ~, and aK （n） the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral ...Let K be an algebraic number field of finite degree over the rational field ~, and aK （n） the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral power sums of aK（n）,This paper is interested in the distribution of integral ideals concerning different number fields. The author is able to establish asymptotic formulae for the convolution sumwhere K1 and K2 are two different quadratic fields.展开更多
This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem.The numerical method is designed for arbitrary spacedependent anisotropy directions and does not require any specially ...This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem.The numerical method is designed for arbitrary spacedependent anisotropy directions and does not require any specially adapted coordinate system.It is also designed to be equally accurate in the strongly and the mildly anisotropic cases.The method is applied to the Euler-Lorentz system,in the drift-fluid limit.This system provides a model for magnetized plasmas.展开更多
文摘This article gives the potential energy function of quark in the gluon field, derives the wave function of quark in stationary state and the quark confinement and asymptotic freedom, shows that a quark is composed of two different color gluons, expounds the formation mechanism of the quark confinement and asymptotic freedom and the physical substance of “colors” of quark, and discusses the stability of hadrons in the end.
基金Project supported by the National Natural Science Foundation of China (Grant No: 10372025) and the National Key Basic Research Foundation (Grant No: 2001CB309400).
文摘The stationary phase method in conventional Lighthill＇s two-stage scheme to get the expressions of the velocity field was given up in this paper. The method that Ursell had used in deducing the elevation expression of ship wave was adopted, and an asymptotic solution of velocity field of ship waves on an inviscid fluid that is perfectly fit for the region inside and outside the critical lines was obtained. It is very convenient to be used in SAR technique.
基金Natural Sciences and Engineering Research Council(NSERC)of Canada。
文摘This paper studies an asymptotic solvability problem for linear quadratic(LQ)mean field games with controlled diffusions and indefinite weights for the state and control in the costs.The authors employ a rescaling approach to derive a low dimensional Riccati ordinary differential equation(ODE)system,which characterizes a necessary and sufficient condition for asymptotic solvability.The rescaling technique is further used for performance estimates,establishing an O(1/N)-Nash equilibrium for the obtained decentralized strategies.
基金supported by National Natural Science Foundation of China(Grant No.11171147)Qing Lan Project,Jiangsu Province,and the Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China(Grant No.708044)
文摘This paper considers the local linear estimation of a multivariate regression function and its derivatives for a stationary long memory(long range dependent) nonparametric spatio-temporal regression model.Under some mild regularity assumptions, the pointwise strong convergence, the uniform weak consistency with convergence rates and the joint asymptotic distribution of the estimators are established. A simulation study is carried out to illustrate the performance of the proposed estimators.
基金The present work is supported by the National Natural Science Foundation of China
文摘The stress and deformation fields near the tip of a mode-I dynamic crack steadily propagating in an elastic-perfectly plastic compressible material are considered under plane strain conditions. Within the framework of infinitesimal displacement gradient theory, the material is characterized by the Von Mises yield criterion and the associated J(2) flow theory of plasticity. Through rigorous mathematical analysis, this paper eliminates the possibilities of elastic unloading and continuous asymptotic fields with singular deformation, and then constructs a fully continuous and bounded asymptotic stress and strain field. It is found that in this solution there exists a parameter phi(0) which cannot be determined by asymptotic analysis but may characterize the effect of the far field. Lastly the variations of continuous stresses, velocities and strains around the crack tip are given numerically for different values of phi(0).
基金Project supported by the National Natural Science Foundation of China(Nos.91430106 and11771040)the Fundamental Research Funds for the Central Universities of China(No.06500073)
文摘The self-similarity solutions of the Navier-Stokes equations are constructed for an incompressible laminar flow through a uniformly porous channel with retractable walls under a transverse magnetic field. The flow is driven by the expanding or contracting walls with different permeability. The velocities of the asymmetric flow at the upper and lower walls are different in not only the magnitude but also the direction. The asymptotic solutions are well constructed with the method of boundary layer correction in two cases with large Reynolds numbers, i.e., both walls of the channel are with suction, and one of the walls is with injection while the other one is with suction. For small Reynolds number cases, the double perturbation method is used to construct the asymptotic solution. All the asymptotic results are finally verified by numerical results.
基金Project(20080431344) supported by Postdoctoral Science Foundation of ChinaProject(51021001) supported by the National Natural Science Foundation of China
文摘A generalized form of material gradation applicable to a more broad range of functionally graded materials(FGMs) was presented.With the material model,analytical expressions of crack tip higher order stress fields in a series form for opening mode and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis.Then,a numerical experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite element analysis by local collocation and then comparing the estimations with the existing solution.The expressions show that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects on crack tip stress fields in the case of FGMs.The numerical experiment further confirms that the addition of the nonhomogeneity specific terms in the expressions not only improves estimates of stress intensity factor,but also gives consistent estimates as the distance away from the crack tip increases.Hence,the analytical expressions are suitable for the representation of crack tip stress fields and the analysis of full field data.
基金supported by the Fundamental Research Funds for the Central Universities(No.14QNJJ004)
文摘Let K be an algebraic number field of finite degree over the rational field ~, and aK （n） the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral power sums of aK（n）,This paper is interested in the distribution of integral ideals concerning different number fields. The author is able to establish asymptotic formulae for the convolution sumwhere K1 and K2 are two different quadratic fields.
基金supported by the Marie Curie Actions of the EuropeanCommission in the frame of the DEASE project(MEST-CT-2005-021122)by the”F´ed´eration de recherche CNRS sur la fusion par confinementmagn´etique”,by theAssociation Euratom-CEA in the framework of the contract”Gyro-AP”(contract#V3629.001 avenant 1)by the University Paul Sabatier in the frame of the contract”MOSITER”.This work was performed while the first author held a post-doctoral position funded by the Fondation”Sciences et Technologies pour l’A´eronautique et l’Espace”,in the frame of the project”Plasmax”(contract#RTRA-STAE/2007/PF/002).
文摘This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem.The numerical method is designed for arbitrary spacedependent anisotropy directions and does not require any specially adapted coordinate system.It is also designed to be equally accurate in the strongly and the mildly anisotropic cases.The method is applied to the Euler-Lorentz system,in the drift-fluid limit.This system provides a model for magnetized plasmas.
